{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T13:38:02Z","timestamp":1762177082744,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T00:00:00Z","timestamp":1519689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51475339"],"award-info":[{"award-number":["51475339"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Natural Science Foundation of Hubei province","award":["2016CFA042"],"award-info":[{"award-number":["2016CFA042"]}]},{"name":"the Applied Basic Research Programs of Wuhan science and technology bureau","award":["2017010201010115"],"award-info":[{"award-number":["2017010201010115"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Dynamic mode decomposition (DMD) is essentially a hybrid algorithm based on mode decomposition and singular value decomposition, and it inevitably inherits the drawbacks of these two algorithms, including the selection strategy of truncated rank order and wanted mode components. A novel denoising and feature extraction algorithm for multi-component coupled noisy mechanical signals is proposed based on the standard DMD algorithm, which provides a new method solving the two intractable problems above. Firstly, a sparse optimization method of non-convex penalty function is adopted to determine the optimal dimensionality reduction space in the process of DMD, obtaining a series of optimal DMD modes. Then, multiscale permutation entropy calculation is performed to calculate the complexity of each DMD mode. Modes corresponding to the noise components are discarded by threshold technology, and we reconstruct the modes whose entropies are smaller than a threshold to recover the signal. By applying the algorithm to rolling bearing simulation signals and comparing with the result of wavelet transform, the effectiveness of the proposed method can be verified. Finally, the proposed method is applied to the experimental rolling bearing signals. Results demonstrated that the proposed approach has a good application prospect in noise reduction and fault feature extraction.<\/jats:p>","DOI":"10.3390\/e20030152","type":"journal-article","created":{"date-parts":[[2018,2,27]],"date-time":"2018-02-27T14:18:08Z","timestamp":1519741088000},"page":"152","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Optimized Dynamic Mode Decomposition via Non-Convex Regularization and Multiscale Permutation Entropy"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5922-0591","authenticated-orcid":false,"given":"Zhang","family":"Dang","sequence":"first","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"},{"name":"National Demonstration Center for Experimental Mechanical Education, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Lv","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yourong","family":"Li","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cancan","family":"Yi","sequence":"additional","affiliation":[{"name":"Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China"},{"name":"Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,2,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.ymssp.2015.08.012","article-title":"SVD and Hankel matrix based de-noising approach for ball bearing fault detection and its assessment using artificial faults","volume":"70\u201371","author":"Golafshan","year":"2016","journal-title":"Mech. 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